{"id":"https://openalex.org/W2963441107","doi":"https://doi.org/10.37236/7281","title":"Distinguishing Graphs of Maximum Valence 3","display_name":"Distinguishing Graphs of Maximum Valence 3","publication_year":2019,"publication_date":"2019-11-22","ids":{"openalex":"https://openalex.org/W2963441107","doi":"https://doi.org/10.37236/7281","mag":"2963441107"},"language":"en","primary_location":{"id":"doi:10.37236/7281","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7281","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p36/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035170291","display_name":"Svenja H\u00fcning","orcid":null},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Svenja H\u00fcning","raw_affiliation_strings":["Graz University of Technology, 8010 Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Graz University of Technology, 8010 Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037896222","display_name":"Wilfried Imrich","orcid":"https://orcid.org/0000-0002-0475-9335"},"institutions":[{"id":"https://openalex.org/I182712176","display_name":"Montanuniversit\u00e4t Leoben","ror":"https://ror.org/02fhfw393","country_code":"AT","type":"education","lineage":["https://openalex.org/I182712176"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Wilfried Imrich","raw_affiliation_strings":["Montanuniversit\u00e4t Leoben, 8700 Leoben, Austria"],"affiliations":[{"raw_affiliation_string":"Montanuniversit\u00e4t Leoben, 8700 Leoben, Austria","institution_ids":["https://openalex.org/I182712176"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028820095","display_name":"Judith Kloas","orcid":null},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Judith Kloas","raw_affiliation_strings":["Graz University of Technology, 8010 Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Graz University of Technology, 8010 Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112456780","display_name":"Hannah Schreber","orcid":null},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hannah Schreber","raw_affiliation_strings":["Graz University of Technology, 8010 Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Graz University of Technology, 8010 Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022919726","display_name":"Thomas W. Tucker","orcid":"https://orcid.org/0000-0002-7868-6925"},"institutions":[{"id":"https://openalex.org/I39660569","display_name":"Colgate University","ror":"https://ror.org/05d23ve83","country_code":"US","type":"education","lineage":["https://openalex.org/I39660569"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas W. Tucker","raw_affiliation_strings":["Colgate University"],"affiliations":[{"raw_affiliation_string":"Colgate University","institution_ids":["https://openalex.org/I39660569"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5035170291"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":null,"apc_paid":null,"fwci":1.3997,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.83531497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"26","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8544212579727173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.776098370552063},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5048428177833557},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.41898757219314575},{"id":"https://openalex.org/keywords/valence","display_name":"Valence (chemistry)","score":0.41362589597702026},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.4101482033729553},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3885602653026581},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05643835663795471}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8544212579727173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.776098370552063},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5048428177833557},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.41898757219314575},{"id":"https://openalex.org/C168900304","wikidata":"https://www.wikidata.org/wiki/Q171407","display_name":"Valence (chemistry)","level":2,"score":0.41362589597702026},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.4101482033729553},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3885602653026581},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05643835663795471},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/7281","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7281","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/7281","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7281","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3288250452","display_name":null,"funder_award_id":"W1230.","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4099270370","display_name":null,"funder_award_id":"Award","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G4135731702","display_name":null,"funder_award_id":"W1230","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4247285292","display_name":null,"funder_award_id":"317689","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G6813351766","display_name":null,"funder_award_id":"FWF W1230","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963441107.pdf","grobid_xml":"https://content.openalex.org/works/W2963441107.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W849813526","https://openalex.org/W1513326856","https://openalex.org/W1516924510","https://openalex.org/W1536407537","https://openalex.org/W1575751884","https://openalex.org/W1843418064","https://openalex.org/W1855706715","https://openalex.org/W1870526072","https://openalex.org/W1965339293","https://openalex.org/W1977019205","https://openalex.org/W2072754781","https://openalex.org/W2097108042","https://openalex.org/W2122198415","https://openalex.org/W2140265961","https://openalex.org/W2167676258","https://openalex.org/W2737519387","https://openalex.org/W2982094579","https://openalex.org/W6655318272","https://openalex.org/W6736117597"],"related_works":["https://openalex.org/W2963257052","https://openalex.org/W4302155387","https://openalex.org/W2949256963","https://openalex.org/W2545189445","https://openalex.org/W2115024785","https://openalex.org/W2949890955","https://openalex.org/W2085781584","https://openalex.org/W4289596368","https://openalex.org/W1543499813","https://openalex.org/W1678473343"],"abstract_inverted_index":{"The":[0],"distinguishing":[1,47],"number":[2,11,48],"$D(G)$":[3],"of":[4,12,40,54],"a":[5,32],"graph":[6],"$G$":[7,39],"is":[8,15],"the":[9,19,23,55],"smallest":[10],"colors":[13],"that":[14,22,59],"needed":[16],"to":[17],"color":[18],"vertices":[20],"such":[21],"only":[24],"color-preserving":[25],"automorphism":[26],"fixes":[27],"all":[28,36,60],"vertices.":[29],"We":[30],"give":[31],"complete":[33],"classification":[34],"for":[35],"connected":[37,62],"graphs":[38,63],"maximum":[41],"valence":[42],"$\\Delta(G)":[43,65],"=":[44,50,66],"3$":[45,67],"and":[46],"$D(G)":[49],"3$.":[51],"As":[52],"one":[53],"consequences":[56],"we":[57],"show":[58],"infinite":[61],"with":[64],"are":[68],"$2$-distinguishable.":[69]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
